NFL Network's Adam Schefter reports that Haley signed a four-year contract.
Haley was introduced at a news conference by team president Clark Hunt and general manager Scott Pioli.
"We really believe he's the right guy for this job," Pioli said.
Haley joins a team that went a franchise-worst 2-14 under coach Herm Edwards, who was fired Jan. 23. Edwards won only two of his last 25 games and launched a rebuilding project that made the Chiefs the league's youngest team this season.
Pioli, hired last month as GM, said Haley has a "strong understanding of players and the type of players that create championship football teams."
Haley called this an "ideal situation" for him and "a chance to work with someone I have experience with in Scott."
The Chiefs haven't won a postseason game since an aging Joe Montana was their quarterback in the 1993 season.
Edwards was considered a players' coach by the Chiefs. Haley can be combative and sometimes clashes with players. He had a first-half argument with Warner, then a short blowup in full view of television cameras with wide receiver Anquan Boldin during the NFC Championship Game against the Eagles,. Haley also had a spat with Terrell Owens when he was the receivers coach in Dallas.
He did not start calling plays until late in the 2007 season. But this season, an Arizona offense led by Warner set a franchise record with 427 points, finished third in scoring in the NFL and was second in passing yards.
"This is a tremendous opportunity for Todd and one that I know he is ready for," said Cardinals coach Ken Whisenhunt. "He was a big part of the offensive success that our team has had over the last two years. Todd is a smart, passionate coach who gets the very best out of players and those attributes will serve him well as a head coach."
"We're interested in getting it right," Haley said, referring to his relationship with Pioli. "We don't care whose idea it is. We just want a solution and an answer."
The hiring completes Hunt's overhaul of the top management rungs of a team he inherited from his father in December 2006. Hunt owns the Chiefs with his sister and two brothers and has ultimate authority as chairman of the board. He accepted Carl Peterson's resignation in December after 20 years as president, chief executive officer and general manager.
Hunt hired Pioli from the New England Patriots' front office and gave him authority over all football matters. Haley and Pioli face issues at just about every position, particularly on defense. Still, conditions seem favorable for the sort of quick turnaround Pioli's father-in-law, Bill Parcells, engineered in Miami.
The Chiefs' 14 losses were by 10 points or fewer, evidence this young team often was only a few plays from a breakthrough.
In addition, Kansas City owns the No. 3 overall pick in the draft and should have plenty of money to work with because it's about $32 million under the salary cap.
Added to that is what amounts to a new stadium. With $250 million in taxpayer money and $125 million from the Hunt family, Arrowhead Stadium is being almost completely renovated. A spruced-up seating area along with swank new offices and weight and training facilities could help attract free agents as well as customers to a stadium often described as the NFL's loudest.
Among Haley's most urgent problems will be disgruntled stars Tony Gonzalez and Larry Johnson. Gonzalez, the all-time leader among tight ends in touchdowns and receptions, said this week at the Pro Bowl he may want out of Kansas City. He was angry during the season that Edwards did not let him get the receiving record at home, and then was upset Peterson would not trade him.
Johnson, the highest-paid player in team history, said this week he saw no future for himself in Kansas City. This season he was benched for violating team rules for three games and suspended for one game by the league. He also faces court dates in two separate cases in which he's charged with simple assault.
A key decision must be made at quarterback. Brodie Croyle, Edwards' choice, has been prone to injury and unreliable. Third-teamer Tyler Thigpen finished the season running the spread offense and was 1-10 as a starter.
The biggest issues, however, are on defense.
Under coordinator Gunther Cunningham, the 2008 Chiefs set an NFL record for pass-rushing futility with only 10 sacks. They also set team records for most yards allowed in a game, most points allowed in a game and biggest lead squandered in a loss. Cunningham has become defensive coordinator for the winless Detroit Lions.
The Associated Press contributed to this report.